What is the volume of a cylinder?
A cylinder is a solid composed of two circular bases (top and bottom). The second base is obtained through the first one, by making a transfer in space. The bases have the same shape and size and most importantly, they have the same area. Schematically speaking, the bases of the cylinder are inscribed in two parallel planes, separated by a distance called the “height”.
The volume of a cylinder is considered to be the product of the area of the base times its height. However, it is important to remember that, if a length is always evaluated in meters and the surface in square meters, the volume is given in cubic meters. The volume of a cylinder is often used to calculate the volume of water filling a cylinder or the space it occupies.
How do you find the volume of a cylinder?
Having to calculate the volume of a three dimensional solid like a cylinder is common in everyday life, whether it is to determine the volume of a container or simply solve a homework, so it’s important to understand the basics. First of all, volume is measured in cubic units, so before you start calculating, you have to make sure that all of the measurements are in the same unit.
To find the volume of a cylinder you have to multiply the area of the base by its height. As stated earlier, the cylinder is made up of two circles that are similar and parallel, so the distance between them is the height. But, when it comes to the area of the circle, it is essential for it to be mentioned in order to calculate the volume. The tricky part is, it is not always mentioned.
To find the area of a cylinder, you must know the radius of the circle referred to as r. The radius connects the point in the center of the circle named O to a given point on the circumference of the diagram named B. Therefore the radius r of the circle is BO. So now that we have the radius of the base we can calculate the area of the circle. The formula of the surface area of the circle is:
A = pi x r ²
A = π x r²
This is the area of the circle.
Volume of Cylinder formula
After determining the area of the circle as well as the height of the cylinder (which is given). It will be possible to use the following formula to calculate the volume of the cylinder:
V = A x height
V = π x r² x h
Example 1 :
Let’s suppose we have a cylinder with a height of 8 cm and a circle radius of 2 cm.
To find the volume of this cylinder, we must find the area first, which in this example is:
A = π x r²
A = 3.14 x 2²
A = 12.56 cm²
And now, let’s calculate the volume of this said cylinder:
V = A x h
V = 12.56 x 8
V = 100.48 cm3
Therefore, the volume of this cylinder is 100.48 cm3
Keep in mind that the numbers stated in this example were in the same units, so if they weren’t, it would be important to convert them.
Example 2 :
In this example, the cylinder has a height of 11 cm and a circle radius of 3 cm.
To find the volume of this cylinder, we must find the total surface area first, which is:
A = π x r²
A = 3.14 x 3²
A = 28.26 cm²
Up next, let’s calculate the volume of the cylinder:
V = A x h
V = 28.26 x 11
V = 310.86 cm3
Therefore, the volume of this cylinder is 310.86 cm3